Consider a random sample of length n for one individual i = 1 with response Yi =
(Y1 , ..., Yn )T and co-variate design matrix


1 xi1

.. 
Xi =  ...
. 
1 xin
with xij ∈ R, j = 1, ..., n. We consider the linear model
Yi = X i β + ξi
with coefficient vector β ∈ R2 and ξi = (ξi1 , ..., ξin )T a random vector of length n with covariance matrix Vi .
Note: For simplicity we assume data was only sampled for a single individual. Nevertheless,
the index ’i’ for the individuals is introduced in preparation for the lecture.
b) Compute Cov(β̂) for the simple least squares estimator β̂ for β.
Datum: Tuesday, 04.05.2017
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